Problem: Three marbles are randomly selected, without replacement, from a bag containing two red, two blue and two green marbles. What is the probability that one marble of each color is selected? Express your answer as a common fraction.
Solution: First, we can find the denominator of our fraction.  There are a total of $\dbinom{6}{3}=20$ ways to choose 3 marbles out of 6.  To find the numerator, we need to count the number of ways to choose one marble of each color.  There are 2 ways we could choose a red marble, 2 ways to choose a blue, and 2 ways to choose a green, making a total of $2\cdot 2 \cdot 2=8$ ways to choose one marble of each color.  Our final probability is $\frac{8}{20}=\boxed{\frac{2}{5}}$.